Lesson 3-5 Compound Inequalities Objective: To solve and graph inequalities containing and o o o or or.

Real-World Connection Do you like to swim? Do you like to swim? Does your family have a swimming pool? Does your family have a swimming pool? Determining how to keep the water in a pool chemically balanced is one way this skill is used in real-world situations. Determining how to keep the water in a pool chemically balanced is one way this skill is used in real-world situations.

Vocabulary compound inequality – two inequalities joined by the word and or the word or compound inequality – two inequalities joined by the word and or the word or solution for and inequalities – (Intersection) any number that makes both inequalities true solution for and inequalities – (Intersection) any number that makes both inequalities true solution for or inequalities – (Union) any number that makes either inequality true solution for or inequalities – (Union) any number that makes either inequality true

STEPS for AND problems 1. Write the compound inequality as two inequalities joined by and. 2. Solve each inequality. 3. Simplify and write the solutions as one statement. 4. Graph the solution.

Example 1, page 161 Write a compound inequality that represents each situation. Graph the solution. Write a compound inequality that represents each situation. Graph the solution. a) all real numbers greater than -2 but less than 9 a) all real numbers greater than -2 but less than 9

You try… b) The books were priced between $3.50 and $6.00, inclusive. b) The books were priced between $3.50 and $6.00, inclusive. Solution: 3.50 < b < 6 Solution: 3.50 < b < 6

Example 2, page 162 Solve each inequality and graph the solution. Solve each inequality and graph the solution. a) -6 < 3x < 15b) -3 < 2x-1 < 7 a) -6 < 3x < 15b) -3 < 2x-1 < 7

You try… Ex. 2c) 7 < -3a + 1 < 13 Ex. 2c) 7 < -3a + 1 < 13 Solution: -4 < n < -2 Solution: -4 < n < -2

Examples with OR (page 163) Ex. 4a) Write an inequality that represents all real numbers that are at most –5 or at least 3. Graph your solution. Ex. 4a) Write an inequality that represents all real numbers that are at most –5 or at least 3. Graph your solution.

To solve OR problems, solve each inequality separately. Ex. 5) Solve –2x + 7 > 3 or 3x – 4 > 5. Ex. 5) Solve –2x + 7 > 3 or 3x – 4 > 5.

Graphic Organizer

Summary What did you learn today? What did you learn today?

Summary Re-write the compound inequality into two problems and solve. Re-write the compound inequality into two problems and solve. For and problems, combine the solutions into one statement. For and problems, combine the solutions into one statement. For or problems, solve each separately. For or problems, solve each separately. Graph. Graph.

Assignment #3-5, page 163, #3-5, page 163, odd & odds 61-69